The Nebula is an award given each year by the Science Fiction and Fantasy Writers of America (SFWA), for the best science fiction stories published in the United States during the two previous years. (See Rolling eligibility below.)
There is no cash prize associated with the award, the award itself being a transparent block with an embedded glitter spiral nebula; however, publishers seldom fail to mention that a novel won the award, and as a mark of acclaim by other science fiction writers, it seems reasonable that the Nebula, like the Hugo award, leads to increased sales.

It often happens, but not predictably, that the writers' award (Nebula) and the fans' award (Hugo) go to the same work.

The fiction Nebulas are awarded in four different categories: novel, novella, novelette, and short story.
The categories are defined by word length, as follows:

Novel: a work of 40,000 words or more

Novella: a work of at least 17,500 words but less than 40,000 words

Novelette: a work of at least 7,500 words but less than 17,500 words

Short story: a work of less than 7,500 words

In addition, a Nebula has been awarded for best dramatic script every year since 1999, but SFWA membership is divided about the appropriateness of the award, and the category may not continue long into the future.

As opposed to the Hugo Award ballot, which is limited to works published during a specific calendar year, the Nebula Awards employ a rolling eligibility system.
Each work is eligible to qualify for the ballot for one year following its date of publication.
During this one-year window, SFWA members can "recommend" the work for the Nebula ballot.
When a work has received ten recommendations, it immediately qualifies for the current year's preliminary Nebula ballot.
Early the following year, SFWA members vote on the works on the preliminary ballot, narrowing the field down to (usually) a final ballot of five works in each category.
Special Nebula juries are permitted, but not required, to add one deserving but overlooked work to the final ballot in each category. SFWA members then vote on the final ballot

As a consequence of rolling eligibility, a work published one year can end up on the subsequent year's Nebula ballot, which is voted on in the year following that.
For example, William Shunn's novelette "Dance of the Yellow-Breasted Luddites" was published in July 2000.
It was eligible to be recommended for the preliminary ballot from its date of publication until the end of June, 2001.
As it happened, the work did not receive the needed tenth recommendation until 2001, so despite its 2000 publication date, it ended up on the 2001 preliminary ballot (and, subsequently, the final ballot).
The 2001 final ballot was then voted upon by SFWA members in 2002.